1

5.1 Formation of Molecular Orbitals (MO’s)from Atomic Orbitals (AO’s)

5. Molecular Orbitals

Ψ = caΨa + cbΨb

Ψ = molecular wave functionΨa and Ψb = atomic wave functionsca and cb = adjustable coefficients

Ψ(σ) = Ν [caΨ(1sa) + cbΨ(1sb)] = 1/√2 [Ψ(1sa) + Ψ(1sb)]

Ψ(σ∗) = Ν [caΨ(1sa) − cbΨ(1sb)] = 1/√2 [Ψ(1sa) − Ψ(1sb)]

for H2

Ha + Hb

Ha - Hb

ca = cb = 1 and N = 1/√2 for σ and σ*Approximation! Remember, an anti-bonding MOis more anti-bonding then a bonding is bonding

5. Molecular Orbitals

ΨΑ−Β = caΨa ± cbΨbThe significance of ca and cb in:

bonding

anti-bonding

…there can be non-bonding orbitals as well!

2

5. Molecular Orbitals

The σ, π and σ*, π* notation

…don’t forget about δ and δ* orbitals!

π π∗

5. Molecular Orbitals

a node between the nuclei!

no node!

5.1.1 MO’s from s-Orbitals

3

5. Molecular Orbitals

however, there can be nodes in bonding MO’sfrom p- and d-orbitals!

5.1.2 MO’s from p-Orbitals

5. Molecular Orbitals

5.1.3 MO’s from d-Orbitals

4

MO-Diagram for the first10 elements:

Works great for O2 -> explainsO2’s paramagnetism

But predicts B2 to be diamagnetic

-> Orbital Mixing!

5.2 Homonuclear Diatomic Molecules

5.2 Homonuclear Diatomic Molecules

B2 is paramagnetic!BO = 1, no σ-bond!

C2 is diamagneticBO = 2, two π-bonds

degenerate orbitals• Aufbau principle• Hund’s Rule• Pauli’s Principle:

effect of orbitalmixing

5

σπ

π∗σ∗

5.2 Homonuclear Diatomic Molecules

Energy of all orbitals decreases as increased nuclear charge attracts the electrons more strongly

Effect is larger for s-orbitals!

Ener

gy

5.2 Homonuclear Diatomic Molecules

6

Bond Distances & Orders, Atomic Number & Radii

5.2 Homonuclear Diatomic Molecules

PhotoelectronSpectroscopy:

O2 + hν -> O2+ + e −

Ionization Energy(binding energy) =

hν − kinetic energyof expelled e

Remember

• Morse-Potential• Vibrational Fine

Structure

5.2 Homonuclear Diatomic Molecules

7

note decreasedspacing with decreased atomic #

5.2 Homonuclear Diatomic Molecules

5.2 Homonuclear Diatomic Molecules

A Correlation Diagram

for Diatomic Molecules

no inter-action

bonding

“fusion”

8

5.3 Heteronuclear Diatomic Molecules

greater nuclear charge, lower energy AO’smore contracted orbitals

MO has mainlyoxygen character

MO has mainlycarbon character

very

impo

rtant*

fille

d bon

ding

MO

very

impo

rtant*

empt

y anti

-

bondin

g M

O’s*CO poisoning& hemoglobinarchitecture

Electronegativity2.54 3.61

5.3 Ionic Compounds& Molecular Orbitals

0.91 4.19Electronegativity

MO has mainlyfluorine pz-character

-> Li+ and F- (p6)

9

5.4 Molecular Orbitalsfor Larger Molecules

5.4.2 Carbon Dioxide’s Molecular Orbital Diagram

O=C=OD∞h

-> D2h

5.4 Molecular Orbitalsfor Larger Molecules

5.4.2 Carbon Dioxide’s Molecular Orbital Diagram

O=C=O

D∞h-> D2h

OxygenGroup Theory

CarbonGroup Theory

10

5.4 Molecular Orbitalsfor Larger Molecules

5.4 Molecular Orbitalsfor Larger Molecules

11

5.4 Molecular Orbitalsfor Larger Molecules

5.4 Molecular Orbitalsfor Larger Molecules

12

5.4 Molecular Orbitalsfor Larger Molecules

et voila... CO2MO Diagram

2σ-bonds

2π-bonds

non-bonding

O=C=O:

:

::

5.4 Molecular Orbitalsfor Larger Molecules

e.g. Water

13

5.4 Molecular Orbitalsfor Larger Molecules

e.g. Ammonia

5.4 Molecular Shapes& Hybrid Orbitals

Combination of Atomic Orbitalsto form Hybrid Orbitals

localized in space& directional

Old but very useful concept!

3x

4x

Try this for NH3, H2O, and CO2